Find the polynomial having roots at $1$ , $1$ , $1$ and $- 2$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - x^{3} - 3 x^{2} + 5 x - 2$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$1$	$x - 1$
$1$	$x - 1$
$- 2$	$x + 2$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (x - 1) \cdot (x - 1) \cdot (x + 2) = x^{4} - x^{3} - 3 x^{2} + 5 x - 2

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Find the polynomial having roots at 1 , 1 , 1 and −2 .

The polynomial generated from the given zeros is: P(x)=x4−x3−3x2+5x−2

Find the polynomial having roots at $1$ , $1$ , $1$ and $- 2$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - x^{3} - 3 x^{2} + 5 x - 2$